e- / DN Uncertainty

[MY PIXEL]

Posted to CCD-world:
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In a message dated 98-01-23 03:32:00 EST, pamico at eso.org writes:

<< Subj:	 A question....
 Date:	98-01-23 03:32:00 EST
 From:	pamico at eso.org (Paola Amico)
 To:	MYPIXEL at AOL.COM
 
 Dear Jim,
 I take advantage of the offer you made us at the CCD Camera course last may
 for asking you a question. Hope it is still valid.........
 
 I am reviewing your notes concerning CCD characterization & testing (Section
 I) and I am puzzled by the result on page 2-12 concerning the Camera gain
 constant uncertainty. Without entering into formulas, I concluded that the
 error affecting the conversion factor should be inversely proportional to
 the total signal received on your test array and not only to the total
 number of pixels. Is there some kind of "normalization" I am missing? 
 
 Thanks a lot,
 
 all the best....................paola amico

 
***************************************************jj

Paola,

Given . . .. 

K (e-/DN) = Signal / (Shot Noise)^2

Variance in K (e-/DN) = 2 K^2 / Np   where Np is the number of pixels sampled


I looked all over for my calculations using the "propagation of errors"
formula for the variance in e-/DN (performed 22 years ago). I have one more
place to look. I sure would like to see your calculations.

For sure the number of pixels is important . . . sampling the signal and shot
noise for one pixel would be very uncertain. Statistics is improved by pixel
count (averages the shot noise by the square-root of the number of pixels
sampled). As for your question about signal . . .  shot noise is going up by
the square-root of signal .. . K is equal to the Signal / (Shot Noise)^2. So
the numerator and denominator are tracking one another. 

K (e-/DN) is also in the equation. A lower voltage camera gain produces a
higher K (e-/DN)  value with less DN count variation (for a fixed average shot
noise).  So I think that is right.

Let's look into those calculations further.

Jim
  
 **********************************jj
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